Baby steps! I understand that often with weight loss you want it to happen quickly, but if you're a picky eater maybe try to start off with introducing new foods into your diet as opposed to solely focusing on weight loss.
Like others have said you're only 13, try not to push yourself too hard, learn to cut yourself some slack. You mentioned impulse control which is why I think it'd be good to go into this slowly. If you try to be too strict and cut out all the "bad" junk food completely the likelihood is that you're going to end up being very unhappy, binging somewhere along the line and that's the last thing you want when trying to lose some weight.
When I was your age I started Slimming World which was fabulous. The main focus of it is purely eating healthier and starting to make better choices, not restricting your intake. There isn't any calorie counting, you have "free" foods which include all your fruits and veggies, you can have as many as you want. Because I was young I was told that I could have one "treat" a day, so a bag of crisps or a bar of chocolate. If you snack a lot try having your one bad treat then fill up on fruit and fat free yoghurt and stuff. But as I said maybe start off trying different foods so you aren't going into a regime where you're forced to eat foods you aren't too keen on or feel you don't have enough choice.
Most importantly try to stay positive and not get too obsessive about it. I'm not saying stuff like Slimming World and not counting calories is the best way, everyone is different, but it might be a good starting point. If you aren't losing weight then maybe tracking your calories is the best way for you but please don't get too hung up on it, it's a slippery slope. Calories are not the be all and end all, they're a guide and it'd probably be more beneficial tracking your macros, so your fat, carb and protein intake. An easy way of doing this is myfitnesspal.com, you can track everything you eat, but again don't be too hard on yourself over numbers.
With regards to exercise try and find something that you enjoy. Even if it isn't a vigorous work out, any activity is better than none. Put your headphones in and go for a walk. If you have access to any consoles you could look into stuff like Wii Fit, or some kind of dancing game like Just Dance. Maybe you have friends that have the same kind of goals, you could discuss walking/jogging together. It's so much easier finding the motivation to do something that has an element of fun.
Think of this as a lifestyle change, not a quick diet fix. Write down why you'd like to lose some weight, talk to your parents if that's a possibility, gain support and of course everyone on here is happy to help. Good luck!